EP0503030B1 - Method of improving vehicle control when braking - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve running stability and vehicle maneuverability by high order running maneuverability control when driving force and braking force are simultaneously controlled. SOLUTION: The improvement method of maneuverability of automobile is provided, and a target value of slip is calculated and controlled by using a wheel control unit. Variables to be measured are: yaw speed ψ', steering angle δ, wheel speed VRi , supply pressure or wheel brake pressure, engine speed, and throttle valve angle. Variables to be estimated are: longitudinal speed of the vehicle VX, longitudinal acceleration of the vehicle VX', wheel sliding value λ1 , longitudinal force FB, tire force FR, and side direction speed VY. he target value λ(i) * can be calculated with these values by using a simple vehicle model.

Description

State of the art

With conventional ABS / ASR systems, the longitudinal dynamics of the vehicle are in the foreground. The stability and manageability of the vehicle are not regulated directly, but result from invariant compromises in the design of the ABS / ASR controller, which cannot be optimal in all driving situations with regard to lateral dynamics and braking distance / acceleration.

From DE-OS 38 40 456 it is known to increase the manageability of a vehicle by determining the slip angle present on the axles and from this deriving target slip values, the observance of which increases the manageability of the vehicle.

Advantages of the invention

Compared to this prior art, a model-based controller design is carried out in the invention. This has the advantage that the controller gains are constantly recalculated according to the driving situation and the road conditions. The two-track model and the tire model used here deliver significantly better results than the otherwise often used single-track models. The controller design is based on a Kalman filter design and is therefore very computationally effective.

In addition, the interventions are carried out on all four wheels, if necessary, and the distribution among the wheels takes place from the point of view of power optimization. The intervention itself takes place by rotating the directions of force on the individual wheels as a result of the changes in slip. Another new feature is the use of multivariable state control. The state variables float angle and yaw rate can be controlled independently of one another within the physical limits.

The overriding driving dynamics control according to the invention improves the driving stability and the controllability of the vehicle while at the same time optimizing the drive / braking force.

For this purpose, a simple, flat model of a four-wheel road vehicle is first derived, on the basis of which a regulation for the driving behavior in all driving conditions is then designed.

The model is of the second order with the state variables yaw rate ψ̇ and slip angle β (see Fig. 1 and Fig. 2 and list of abbreviations at the end of the description).

(V _X Längsgeschwindigkeit, V _Y Quergeschwindigkeit)
Damit gilt für die zeitliche Änderung:

Für Relativbewegungen gilt:
${\dot{\mathit{\text{V}}}}_{\mathit{\text{Y}}}\text{=}{\mathit{\text{a}}}_{\mathit{\text{Y}}}\text{-}\dot{\text{ψ}}\text{·}{\mathit{\text{V}}}_{\mathit{\text{X}}}$

, wobei a _Y die Querbeschleunigung ist.The following applies to the float angle:

( V _X longitudinal speed, V _Y transverse speed)
The following applies to the change over time:

The following applies to relative movements:
${\dot{\mathit{\text{V}}}}_{\mathit{\text{Y}}}\text{=}{\mathit{\text{a}}}_{\mathit{\text{Y}}}\text{-}\dot{\text{ψ}}\text{·}{\mathit{\text{V}}}_{\mathit{\text{X}}}$

, where a _{Y is} the lateral acceleration.

Die Querbeschleunigung a _Y läßt sich aus der Summe der an den Reifen quer auf das Fahrzeug wirkenden Kräfte F _Y ermitteln (s. Fig. 2).

mit m = Fahrzeugmasse.So the differential equation for the float angle is:

The lateral acceleration a _Y can be determined from the sum of the forces F _Y acting transversely on the tires on the vehicle (see FIG. 2).

with m = vehicle mass.

mit

Die Differentialgleichung für die Giergeschwindigkeit ergibt sich aus den um den Fahrzeugschwerpunkt wirkenden Momenten aus Reifenkräften und den entsprechenden Hebelarmen (s. Fig. 2):

mit $$\begin{array}{c}\begin{array}{c}{\mathit{\text{F}}}_{\mathit{\text{X}}}{\text{}}_{\text{1}}\text{=cosδ·}{\mathit{\text{F}}}_{\mathit{\text{B}}}{\text{}}_{\text{1}}\text{-sinδ·}{\mathit{\text{F}}}_{\mathit{\text{S}}}{\text{}}_{\text{1}}\\ {\mathit{\text{F}}}_{\mathit{\text{X}}}{\text{}}_{\text{3}}{\text{=F}}_{\text{B3}}\\ {\mathit{\text{F}}}_{\mathit{\text{Y}}}{\text{}}_{\text{1}}\text{=cosδ·}{\mathit{\text{F}}}_{\mathit{\text{S}}}{\text{}}_{\text{1}}\text{+sinδ·}{\mathit{\text{F}}}_{\mathit{\text{B}}}{\text{}}_{\text{1}}\end{array}\end{array}$$

usw.To determine the lateral forces at a steering angle δ not equal to zero, the longitudinal ( F _B ) and the lateral forces ( F _S ) on the tires must be taken into account on the front wheels.

With

The differential equation for the yaw rate results from the moments of tire forces acting around the center of gravity of the vehicle and the corresponding lever arms (see Fig. 2):

With $$\begin{array}{c}\begin{array}{c}{\mathit{\text{<figure-callout id="1" label="F X" filenames="imgf0002.png" state="{{state}}">F </figure-callout>}}}_{\mathit{\text{X}}}{}_{\text{1}}\text{= cosδ}{\mathit{\text{F}}}_{\mathit{\text{B}}}{}_{\text{1}}\text{-sinδ}{\mathit{\text{F}}}_{\mathit{\text{S}}}{}_{\text{1}}\\ {\mathit{\text{F}}}_{\mathit{\text{X}}}{}_{\text{3rd}}{\text{= F}}_{\text{B3}}\\ {\mathit{\text{<figure-callout id="1" label="F Y" filenames="imgf0002.png" state="{{state}}">F </figure-callout>}}}_{\mathit{\text{Y}}}{}_{\text{1}}\text{= <figure-callout id="1" label="cosδ F S" filenames="imgf0002.png" state="{{state}}">cosδ </figure-callout>}{\mathit{\text{F}}}_{\mathit{\text{S}}}{}_{}{}_{\text{1}}\text{+ sinδ ·}{\mathit{\text{<figure-callout id="1" label="F B" filenames="imgf0002.png" state="{{state}}">F </figure-callout>}}}_{\mathit{\text{B}}}{}_{\text{1}}\end{array}\end{array}$$

etc.

mit

Die Reifenkräfte erhält man bei bekanntem Reifenschlupf und Schräglaufwinkel näherungsweise aus folgender Beziehung:

mit (s. Fig. 3)

Es folgt:

Zwischen dem resultierenden Reifenschlupf S _i und dem resultierenden Kraftschlußbeiwert » _Ri gibt es einen ähnlichen nichtlinearen Zusammenhang wie zwischen dem bekannten Reifenschlupf λ und dem Kraftschlußbeiwert » in Reifenlängsrichtung. Im folgenden wird davon ausgegangen, daß der Reifen während der ABS-Regelung im allg. den Bereich der Sättigung nicht verläßt, d.h. daß S größer ist als S _min (s. Fig. 4). Das kann durch genügend großen Schlupf und/oder durch genügend großen Schräglaufwinkel an den Rädern erreicht werden. Damit wird sichergestellt, daß die zwischen Fahrbahn und Reifen maximal übertragbare Gesamtkraft (aufgeteilt in Längs- und Querkraft) weitgehend ausgenutzt wird.So:

With

With known tire slip and slip angle, the tire forces are obtained approximately from the following relationship:

with (see Fig. 3)

It follows:

There is a similar non-linear relationship between the resulting tire slip S _i and the resulting adhesion coefficient » _Ri as between the known tire slip λ and the adhesion coefficient» in the longitudinal direction of the tire. In the following it is assumed that the tire generally does not leave the saturation range during the ABS control, ie that S is greater than S _min (see FIG. 4). This can be achieved by a sufficiently large slip and / or by a sufficiently large slip angle on the wheels. This ensures that the maximum total force that can be transmitted between the road and the tire (divided into longitudinal and lateral forces) is largely used.

The size of the total force F _R of each tire remains approximately constant in the range S > S _min . By changing the tire slip or (indirectly via a rotation of the vehicle) the slip angle, the direction of the resulting total force can be changed. The effect of the vehicle controller described here is based on this change in the force directions and, as a result, on the longitudinal and transverse forces and yaw moments acting on the vehicle.

The slip angle α _i on the tires can be specified as a function of the state variables float angle β and the yaw rate ψ̇ and the steering angle δ (see FIG. 5).

Da ψ̇·l _L klein ist gegenüber V _X kann vereinfacht werden zu:

mit

Ebenso kann vorne rechts und hinten verfahren werden.For example, the front left applies:

Since ψ̇ · l _{L is} small compared to V _{X it} can be simplified to:

With

The same can be done at the front right and rear.

mit

Aus (1), (2) und (3) und mit (4), (5), (7) und (8) ergeben sich damit folgende Systemgleichungen:

mit (9) $${\text{α}}_{\mathit{\text{i}}}{\text{=β+e}}_{\mathit{\text{i}}}\dot{\text{ψ}}{\text{+d}}_{\mathit{\text{i}}}\text{δ}$$

Die Giergeschwindigkeit kann mit geeigneten Sensoren, z.B. Faserkreisel, direkt gemessen werden.The following applies to the slip angle: $$\underline{\text{α}}\text{=}\underline{\text{1}}\text{· Β +}\underline{\text{e}}\text{·}\dot{\text{ψ}}\text{+}\underline{\text{d}}\text{· Δ}$$

With

The following system equations result from (1), (2) and (3) and with (4), (5), (7) and (8):

with (9) $${\text{α}}_{\mathit{\text{i}}}{\text{= β + e}}_{\mathit{\text{i}}}\dot{\text{ψ}}{\text{+ d}}_{\mathit{\text{i}}}\text{δ}$$

The yaw rate can be measured directly using suitable sensors, such as fiber gyroscopes.

The steering angle can also be measured using already known devices.

The float angle and the tire forces can be approximately determined in conjunction with a suitable wheel slip controller using an estimation algorithm (observer). Such an observer is described in patent application P 40 30 653.4.

Longitudinal vehicle speed and acceleration are approximately known from the wheel speed sensors present in ABS / ASR devices and a corresponding evaluation, as are the instantaneous wheel slip values on the individual wheels (patent application P 40 24 815.1). The slip values form the manipulated variable of the controller because they can be influenced via the brake pressure.

The parameters steering angle, vehicle speed and acceleration and the resulting tire forces are assumed to be slowly changing and thus quasi-stationary.

Estimated values can be assumed for the vehicle parameters mass, moment of inertia, center of gravity and tire stiffness.

The second-order vehicle model is thus completely known and can be used as the basis for a controller design.

To do this, the system is first linearized around working points that change over time. Physically realizable values for the slip angle β and the yaw rate ψ̇, e.g. the currently desired values.

mit

Nonlinear system: $$\underline{\dot{\mathit{\text{Y}}}}\text{=}\mathit{\text{f}}\text{(}\underline{\mathit{\text{Y}}}\text{,}\underline{\text{λ}}\text{,}\mathit{\text{t}}\text{)}$$

With

Der Linearisierungsfehler r wird vernachlässigt.Linearization:
Operating points of the state variables Y (e.g. target trajectory): Y ₀ ( t )
Working points of the manipulated variables λ (e.g. working point of a subordinate wheel slip controller , without intervention by the vehicle controller ): λ₀ ( t )

The linearization error r is neglected.

Die Systemgleichung des linearisierten Systems lautet damit: $$\underline{\dot{\mathit{\text{X}}}}\text{=A}\underline{\mathit{\text{X}}}\text{+}\mathit{\text{B}}\underline{\mathit{\text{U}}}\text{'+}\underline{\mathit{\text{Z}}}$$

mit

Der Term Z wird wie eine Störgröße behandelt, die über die Stellgröße kompensiert werden kann.Two pseudo input variables U 1 'and U 2' are initially formed for the controller design.

The system equation of the linearized system is therefore: $$\underline{\dot{\mathit{\text{X}}}}\text{= A}\underline{\mathit{\text{X}}}\text{+}\mathit{\text{B}}\underline{\mathit{\text{U}}}\text{'+}\underline{\mathit{\text{Z.}}}$$

With

The term Z is treated like a disturbance variable that can be compensated for via the manipulated variable.

Für die Störgrößenaufschaltung gilt: $$\underline{{\mathit{\text{U}}}_{\mathit{\text{Z}}}}\text{=-}\mathit{\text{B}}\text{⁻¹·}\underline{\mathit{\text{Z}}}\text{=-}\underline{\mathit{\text{Z}}}$$

Der Reglerentwurf wird durchgeführt für: $$\underline{\dot{\mathit{\text{X}}}}\text{=}\mathit{\text{A}}\text{·}\underline{\mathit{\text{X}}}\text{+}\mathit{\text{B}}\text{·}\underline{\mathit{\text{U}}}$$

Wenn um die Sollwerte linearisiert wird, dann entfällt eine Führungsgrößenaufschaltung. Das Regelgesetz lautet dann: $$\underline{\mathit{\text{U}}}\text{=-}\mathit{\text{F}}\text{·}\underline{\mathit{\text{X}}}$$

Die Zustandsgrößenrückführmatrix F kann z.B. mit dem bekannten Riccati-Entwurf berechnet werden.For the controller design, the manipulated variables U 'are divided into the state variable feedback U and the disturbance variable feed-in U _Z. $$\underline{\mathit{\text{U}}\text{'}}\text{=}\underline{\mathit{\text{U}}}\text{+}\underline{{\mathit{\text{U}}}_{\mathit{\text{Z.}}}}$$

The following applies to the feedforward control: $$\underline{{\mathit{\text{U}}}_{\mathit{\text{Z.}}}}\text{= -}\mathit{\text{B}}\text{⁻¹ ·}\underline{\mathit{\text{Z.}}}\text{= -}\underline{\mathit{\text{Z.}}}$$

The controller design is carried out for: $$\underline{\dot{\mathit{\text{X}}}}\text{=}\mathit{\text{A}}\text{·}\underline{\mathit{\text{X}}}\text{+}\mathit{\text{B}}\text{·}\underline{\mathit{\text{U}}}$$

If linearization is carried out around the setpoints, there is no reference variable. The rule law is then: $$\underline{\mathit{\text{U}}}\text{= -}\mathit{\text{F}}\text{·}\underline{\mathit{\text{X}}}$$

The state variable feedback matrix F can be calculated, for example, using the known Riccati design.

Eine Euler-Diskretisierung ergibt: $$\underline{\mathit{\text{X}}}{\text{}}_{\mathit{\text{K}}}{\text{}}_{\text{+1}}{\text{=Φ}}_{\mathit{\text{K}}}\text{·}\underline{\mathit{\text{X}}}{\text{}}_{\mathit{\text{K}}}\text{+}\underline{\widehat{\mathit{\text{U}}}}{\text{}}_{\mathit{\text{K}}}$$

mit $${\text{Φ}}_{\mathit{\text{K}}}\text{=}\mathit{\text{T}}\text{·}\mathit{\text{A}}\text{+}\mathit{\text{I}}\text{;}\underline{\widehat{\mathit{\text{U}}}}{\text{}}_{\mathit{\text{K}}}\text{=}\mathit{\text{T}}\text{·}\underline{\mathit{\text{U}}}$$

mit T: Abtastzeit
Die Zustandsrückführung wird zu $$\underline{\widehat{\mathit{\text{U}}}}{\text{}}_{\mathit{\text{K}}}\text{=-}{\mathit{\text{F}}}_{\mathit{\text{K}}}\text{·}\underline{\mathit{\text{X}}}{\text{}}_{\mathit{\text{K}}}$$

gewählt.Known iterative and non-iterative methods are available to solve the nonlinear Matrix-Riccati equation. With the iterative methods, the numerical difficulties should not be underestimated, especially with regard to a real-time design, non-iterative methods differ from the outset due to the high numerical effort for determining the eigenvalues ​​and eigenvectors of the Hamiltonian canonical system. A method for determining optimal state feedbacks has therefore been developed which avoids the difficulties mentioned above. The starting point is the system listed above (15). $$\underline{\dot{\mathit{\text{X}}}}\text{=}\mathit{\text{A}}\underline{\mathit{\text{X}}}\text{+}\underline{\mathit{\text{U}}}$$

Euler discretization results in: $$\underline{\mathit{\text{X}}}{}_{\mathit{\text{K}}}{}_{\text{+1}}{\text{= Φ}}_{\mathit{\text{K}}}\text{·}\underline{\mathit{\text{X}}}{}_{\mathit{\text{K}}}\text{+}\underline{\widehat{\mathit{\text{U}}}}{}_{\mathit{\text{K}}}$$

With $${\text{Φ}}_{\mathit{\text{K}}}\text{=}\mathit{\text{T}}\text{·}\mathit{\text{A}}\text{+}\mathit{\text{I.}}\text{;}\underline{\widehat{\mathit{\text{U}}}}{}_{\mathit{\text{K}}}\text{=}\mathit{\text{T}}\text{·}\underline{\mathit{\text{U}}}$$

with T : sampling time
The status feedback becomes $$\underline{\widehat{\mathit{\text{U}}}}{}_{\mathit{\text{K}}}\text{= -}{\mathit{\text{F}}}_{\mathit{\text{K}}}\text{·}\underline{\mathit{\text{X}}}{}_{\mathit{\text{K}}}$$

chosen.

Die Rückführmatrix F _K soll nun so bestimmt werden, daß gilt:

mit G: Gewichtungsmatrix, diagonal positiv definit.So: $$\underline{\mathit{\text{X}}}{}_{\mathit{\text{K}}}{}_{\text{+1}}{\text{= (Φ}}_{\mathit{\text{K}}}\text{-}{\mathit{\text{F}}}_{\mathit{\text{K}}}\text{)}\underline{\mathit{\text{X}}}{}_{\mathit{\text{K}}}$$

The feedback matrix F _K should now be determined such that:

with G : weighting matrix, diagonally positive defin.

mit

so folgt aus (17):

Führt man den neuen Zustandsvektor $$\underline{\mathit{\text{Z}}}{\text{}}_{\mathit{\text{K}}}\text{=}\mathit{\text{M}}\text{·}\underline{\mathit{\text{X}}}{\text{}}_{\mathit{\text{K}}}$$

ein so folgt aus (16):

und aus (18):

mit

Vergleicht man (19) mit der Schätzfehlergleichung eines Beobachters und dem dazughörigen Gütekriterium

so sind bei Wahl von C=1 (19) und (20) formal gleichwertig. Das bedeutet, daß zur Berechnung von F $\genfrac{}{}{0ex}{}{\mathit{\text{*}}}{\mathit{\text{K}}}$

Algorithmen zur Berechnung optimaler Zustandsbeobachter eingesetzt werden können. Dabei bietet sich das Kalman-Filter aufgrund seiner rekursiven Struktur besonders an.You choose $$\mathit{\text{G}}\text{=}\mathit{\text{M}}\text{·}\mathit{\text{M}}$$

With

it follows from (17):

If one leads the new state vector $$\underline{\mathit{\text{Z.}}}{}_{\mathit{\text{K}}}\text{=}\mathit{\text{M}}\text{·}\underline{\mathit{\text{X}}}{}_{\mathit{\text{K}}}$$

one follows from (16):

and from (18):

With

If we compare (19) with the estimation error equation of an observer and the associated quality criterion

if C = 1 (19) and (20) are formally equivalent. This means that to calculate F $\genfrac{}{}{0ex}{}{\mathit{\text{*}}}{\mathit{\text{K}}}$

Algorithms for the calculation of optimal condition observers can be used can. The Kalman filter is particularly suitable due to its recursive structure.

lauten:

mit

Die Eingangsgröße in Gleichung (15) ergibt sich damit zu:

Bei der Umrechnung der zwei Pseudo-Eingangsgrößen U ' (14) in die vier Stellgrößen Δλ stehen zwei Freiheitsgrade zur Verfügung. Diese können dazu verwendet werden, die Längsverzögerung und damit die Bremskraft in Fahrzeuglängsrichtung zu maximieren, um bei vorgegebenem Fahrzeugverhalten (bezüglich Seiten- und Gierbewegung) einen möglichst kurzen Bremsweg zu erzielen.The equations for calculating F $\genfrac{}{}{0ex}{}{\mathit{\text{*}}}{\mathit{\text{K}}}$

ring:

With

The input variable in equation (15) thus results in:

Two degrees of freedom are available when converting the two pseudo input variables U '(14) into the four manipulated variables Δλ . These can be used to maximize the longitudinal deceleration and thus the braking force in the longitudinal direction of the vehicle in order to achieve the shortest possible braking distance for a given vehicle behavior (with respect to lateral and yaw movement).

oder mit (3), (7) und (8):

mit $${\text{λ}}_{\mathit{\text{i}}}{\text{=λ}}_{\mathit{\text{0i}}}{\text{+Δλ}}_{\mathit{\text{i}}}$$

Für die maximale Längsverzögerung gilt:

Als Nebenbedingungen der Minimierungsaufgabe müssen die Gleichungen (12) erfüllt werden:

Außerdem müssen Beschränkungen der Variablen λ _i beachtet werden, da der Radbremsschlupf nur Werte zwischen Null und Eins annehmen kann.

Die Sollwerte für den Schwimmwinkel β und für die Giergeschwindigkeit ψ̇ können entsprechend dem gewünschten Fahrverhalten festgelegt werden. Der vom Fahrer durch den Lenkwinkel vorgegebene Wunsch zur Richtungsänderung muß dabei unter Berücksichtigung der Fahrzeuggeschwindigkeit und der Fahrbahnverhältnisse in entsprechende Sollwerte umgerechnet werden.The equation for the longitudinal acceleration is (see Fig. 2).

or with (3), (7) and (8):

With $${\text{λ}}_{\mathit{\text{i}}}{\text{= λ}}_{\mathit{\text{0i}}}{\text{+ Δλ}}_{\mathit{\text{i}}}$$

The following applies to the maximum longitudinal deceleration:

As ancillary conditions for the minimization task, equations (12) must be fulfilled:

In addition, restrictions of the variable λ _i must be observed, since the wheel brake slip can only take values between zero and one.

The setpoints for the float angle β and for the yaw rate ψ̇ can be set according to the desired driving behavior. The driver's wish for a change of direction, as determined by the steering angle, must be converted into corresponding target values, taking into account the vehicle speed and the road conditions.

Example:

V _Ch ist dabei eine Konstante, die das Fahrverhalten bei höheren Geschwindigkeiten beeinflußt. Dieser Rohwert muß bei großem Lenkwinkel, hoher Fahrzeuggeschwindigkeit oder niedrigem Haftreibbeiwert der Fahrbahn auf einen sinnvollen Wert begrenzt werden, da sonst die Giergeschwindigkeit größer wird als die maximal mögliche Winkeländerungsgeschwindigkeit der Bahnkurve. Dann nimmt der Schwimmwinkel zu und das Fahrzeug schleudert.Setpoint for ψ̇:

V _Ch is a constant that influences driving behavior at higher speeds. With a large steering angle, high vehicle speed or low coefficient of static friction on the road, this raw value must be limited to a reasonable value, since otherwise the yaw rate will be greater than the maximum possible angular rate of change of the path curve. Then the float angle increases and the vehicle skids.

mit $$\text{0<}{\mathit{\text{f}}}_{\mathit{\text{Y}}}\text{<1}$$

Daraus läßt sich dann eine maximale Giergeschwindigkeit für stationäre Kurvenfahrt berechnen.

Für den Schwimmwinkel können neben echten Sollwerten auch Begrenzungen vorgegeben werden, die verhindern, daß der Schwimmwinkel zu groß wird. Eine Regelabweichung der ersten Zustandsgröße ergibt sich in diesem Fall nur, wenn der Betrag des Schwimmwinkels seine Begrenzung überschreitet. Die Begrenzung kann z.B. so festgelegt werden, daß bei Bremsschlupf Null der resultierende Schlupf S an den Hinterrädern die Sättigungsgrenze S _min nicht wesentlich überschreitet (s. Fig. 4, (6)).To avoid this, it is determined, for example, what proportion of the maximum available total force the shear force may use.

With $$\text{0 <}{\mathit{\text{f}}}_{\mathit{\text{Y}}}\text{<1}$$

A maximum yaw rate for stationary cornering can then be calculated from this.

In addition to real setpoints, limits can also be specified for the float angle, which prevent the float angle from becoming too large. In this case, there is a control deviation of the first state variable only if the amount of the float angle exceeds its limit. The limitation can be determined, for example, so that when the brake slip is zero, the resulting slip S on the rear wheels does not significantly exceed the saturation limit S _min (see FIG. 4, (6)).

The vehicle controller described above can be used with an algorithm for estimating the vehicle speed and the tire forces (P 40 30 653.4, Appendix I) and with another algorithm for setting the target slip values on the individual wheels specified by the vehicle controller (e.g. patent application P 40 30 724.7 Appendix III, and P 40 24 815.1, Appendix II) can be combined. 6 shows an overview of the overall system in ABS.

_X . Damit sind auch die Radschlupfwerte der einzelnen Räder bekannt. Mit diesen Informationen kann der Beobachter 3 die Fahrzeugguergeschwindigkeit V̂ _Y und die Seitenkräfte F̂ _s an den Reifen und damit auch die resultierenden Reifenkräfte F̂ _R abschätzen. Damit sind alle Größen bekannt, die ein Fahrzeugregler 4 nach der oben beschriebenen Methode zur Bestimmung der Sollschlupfwerte λ _soll benötigt. Die Sollschlupfwerte werden dann an den Schlupfregler 2 weitergegeben, der sie durch Änderung der Radbremsdrücke P _i mittels der Bremshydraulik 5 einstellt. Bei ASR-Reglern kann außerdem das Motormoment durch den Regler verändert werden.The steering angle δ and the adhesion coefficient »₀ act on the vehicle 1 from the outside. On the vehicle 1, the wheel speeds V _Ri , the steering angle δ and the yaw rate ψ̇ are measured, as well as possibly the admission pressure P of the brake system or the individual wheel brake cylinder pressures P _i . With ASR controllers, for example, the engine speed and the throttle valve angle are also measured. A slip controller 2 estimates therefrom with the aid of the variables supplied by an observer 3, the braking forces F _B and the longitudinal vehicle speed V _X and acceleration

_X. The wheel slip values of the individual wheels are thus also known. With this information, the observer 3 can check the vehicle speed V̂ _Y and the lateral forces F̂ _s on the tires and thus also estimate the resulting tire forces F̂ _R. To ensure that all variables are known, which _should λ a vehicle controller 4 according to the method described above for determining the target slip values needed. The setpoint slip values are then passed on to the slip controller 2, which adjusts them by changing the wheel brake pressures P _i by means of the brake hydraulics 5. For ASR controllers, the engine torque can also be changed by the controller.

7 shows a rough flowchart of the method as an example.

This method can be implemented in a programming language and implemented on a suitable digital computer (microprocessor). Compared to conventional ABS / ASR systems, it offers increased vehicle stability (safe prevention of skidding), improved steerability with steering behavior that can be specified by the setpoints, and better steering potential utilization of the road surface during steering maneuvers and thus a shorter braking distance or better vehicle acceleration. The compromises necessary with conventional systems to master all driving and road situations that occur are largely eliminated.

The control concept described here can be used in all driving situations, not only in ABS / ASR operation.

_X , Bremskräfte F̂ _Bi und Schlupfwerte λ_i abgeschätzt (z.B. gemäß Anlage I). Ein Beobachter 13 schätzt hieraus die Reifenkräfte F̂ _R und die Quergeschwindigkeit V̂ _Y . Hieraus können in einem Block 14 die Werte für den Schwimmwinkel β, die Schräglaufwinkel α _i und den Minimalschlupf S _min ermittelt werden. Hieraus ergeben sich dann in einem Block 15 die Sollwerte β _soll und ψ̇ _soll .Block 10 represents the vehicle. The wheel speeds V _Ri , the yaw rate ψ̇, the steering angle δ and the admission pressure P or the wheel brake pressures P _{i are} measured with a block 11 measuring technique. In a slip controller 12, the variables are the longitudinal velocity V Längs _X , longitudinal acceleration

_X , braking forces F̂ _Bi and slip values λ _i estimated (e.g. according to Appendix I). An observer 13 estimates from this the tire forces F̂ _R and the transverse speed V̂ _Y. From this, the values for the slip angle β, the slip angle α _i and the minimum slip S _min can be determined in a block 14. This results then in a block 15 _to the target values β and ψ̇ _{is intended.}

und

welche den Einfluß von Schlupfänderungen auf das Systemverhalten beschreiben.In block 16, the now well-known measuring and estimated values, the vehicle parameters (such as vehicle mass m) and the setpoint values used herein as operating points Y ₀ are _intended β and ψ̇ _{is to} inserted into the already calculated in advance Linearization equations of the vehicle model. The system matrix A and the amplification factors are thus obtained

and

which describe the influence of slip changes on the system behavior.

In block 17, a controller design can be carried out for the now known, linearized system (see equation (15)) as described and the state variable feedback matrix F is obtained .

In block 18, the pseudo manipulated variable U 'is calculated from the control deviation X , the feedback matrix F and the feedforward control U _Z (see equation (14)). According to the described method of longitudinal force optimization, the slip values λ _should now _be calculated in such a way that the desired manipulated variables U 'are realized (see equation 12).

The slip setpoints are again fed to the slip controller 12, which converts them into brake pressures P _i via the brake hydraulics 20.

The vehicle control concept described so far can be changed or expanded if necessary.

If the vehicle is equipped accordingly, the control concept described can be used to control the steering angle on the rear wheels in addition to the wheel slip values. To do this, an additional variable δ _H must be introduced for the rear wheel steering angle.

mit $${\text{cosδ}}_{\mathit{\text{H}}}\mathit{\text{=}}{\text{1 ; sinδ}}_{\mathit{\text{H}}}{\mathit{\text{=δ}}}_{\mathit{\text{H}}}$$

Die Definition (3) werden ergänzt durch:

Die Gleichung (4) für die Gierbeschleunigung lautet nun:

Die Definitionen (5) werden ergänzt durch:

Die Gleichung (8) für die Schräglaufwinkel lautet nach Einführung des Hinterradwinkels: $$\underline{\text{α}}\text{=}\underline{\text{1}}\text{·β+}\underline{\mathit{\text{e}}}\text{·}\dot{\text{ψ}}\text{+}\underline{\mathit{\text{d}}}\text{·δ+}\underline{{\mathit{\text{d}}}_{\mathit{\text{H}}}}{\text{·δ}}_{\mathit{\text{H}}}$$

mit der zusätzlichen Definition (9):

Die Linearisierung des Systems $$\underline{\dot{\mathit{\text{Y}}}}\text{=}\underline{\mathit{\text{f}}}\text{(}\underline{\mathit{\text{Y}}}\text{,}\underline{\text{λ}}{\text{,δ}}_{\mathit{\text{H}}}\text{,}\mathit{\text{t}}\text{)}$$

muß zusätzlich für die neue Stellgröße δ _H durchgeführt werden, wobei als Arbeitspunkt ${\text{δ}}_{\mathit{\text{H}}}{\text{}}_{\text{0}}\text{=0}$

gewählt werden kann.After linearization of δ _H by δ _H = 0, the equation for the lateral acceleration (2) is:

With $${\text{cosδ}}_{\mathit{\text{H}}}\mathit{\text{=}}{\text{1 ; sinδ}}_{\mathit{\text{H}}}{\mathit{\text{= δ}}}_{\mathit{\text{H}}}$$

The definition (3) is supplemented by:

The equation (4) for yaw acceleration is now:

The definitions (5) are supplemented by:

The equation (8) for the slip angle is after the introduction of the rear wheel angle: $$\underline{\text{α}}\text{=}\underline{\text{1}}\text{· Β +}\underline{\mathit{\text{e}}}\text{·}\dot{\text{ψ}}\text{+}\underline{\mathit{\text{d}}}\text{Δ +}\underline{{\mathit{\text{d}}}_{\mathit{\text{H}}}}{\text{· Δ}}_{\mathit{\text{H}}}$$

with the additional definition (9):

The linearization of the system $$\underline{\dot{\mathit{\text{Y}}}}\text{=}\underline{\mathit{\text{f}}}\text{(}\underline{\mathit{\text{Y}}}\text{,}\underline{\text{λ}}{\text{, δ}}_{\mathit{\text{H}}}\text{,}\mathit{\text{t}}\text{)}$$

must also be carried out for the new manipulated variable δ _H , using the operating point ${\text{δ}}_{\mathit{\text{H}}}{}_{\text{0}}\text{= 0}$

can be chosen.

Für die Bremskraftoptimierung steht damit ein zusätzlicher, dritter Freiheitsgrad zur Verfügung.The equations (12) for the pseudo input variables are then:

An additional, third degree of freedom is therefore available for brake force optimization.

In addition to the target trajectory, the linearization of the system (10), (11) can also be carried out around other operating points of the state variables Y ₀ , for example around the undisturbed natural movement of the system. In this case, in addition to the state variable feedback matrix F , a reference variable feedback matrix W must also be calculated, since the operating point and setpoint do not match. As a working point for the manipulated variables λ₀ , for example, the respective actual value of the slip can also be selected.

In addition to the Riccati design and the controller design described above using Kalman filters, another controller design process can also be used, e.g. with the help of a pole specification.

und $$\text{λ₃-λ₀₃=λ₄-λ₀₄}$$

keine Freiheitsgrade mehr zur Verfügung stehen.There are also less computing-intensive alternatives for the braking force optimization described above, which lead to only slightly poorer results. For example, the same target slip value can be specified on the left and right front and rear wheels. With approximately equal slip angles left and right according to equation (7), the ratio of lateral to braking force and thus the direction of the resulting force F _Ri left and right is almost the same. The longitudinal deceleration achieved is only slightly less than that which can be achieved through full optimization. The optimization is omitted because of the two constraints $$\text{λ₁-λ₀₁ = λ₂-λ₀₂}$$

and $$\text{λ₃-λ₀₃ = λ₄-λ₀₄}$$

degrees of freedom are no longer available.

Optimization can also be simplified if you do not specify slip changes on all wheels. Good control results can already be achieved, for example, if braking is only applied to the front wheel on the outside of the curve and the rear wheel on the inside of the curve. These two wheels help control yaw rate generally much more than the wheels of the other vehicle diagonals.

Dies muß beim Reglerentwurf berücksichtigt werden. Auch mit nur einer Stellgröße ist das System vollständig steuerbar. Zur Bremskraftoptimierung muß nur die zweite Gleichung in (12) berücksichtigt werden.The same applies to the optimization of vehicle acceleration. In many cases it is possible to dispense with the input variable U'₁ entirely. The input matrix is then:

This must be taken into account when designing the controller. The system can be fully controlled even with just one manipulated variable. To optimize braking force, only the second equation in (12) has to be taken into account.

If the model parameters are not known well enough anyway, the disturbance variables Z (13) can be neglected without the control quality suffering as a result.

In special cases, such as very different static friction coefficients of the road under the left and right wheels, additional measures may be necessary to achieve satisfactory driving behavior. The control concept described above, in which the area of tire saturation must not be left (see FIG. 4), can in such cases lead to excessive yaw movement and thus to vehicle instability. Improvements can be achieved by limiting the pressure differences or the braking force differences on the rear wheels.

The permissible differences can be constant or increase in a controlled manner after the start of braking. Such solutions are already known under the name yaw moment weakening or yaw moment build-up delay. Since the braking forces and the yaw movement are known in the control concept presented here However, depending on the driving condition, more specific permissible braking force differences can be specified.

If a subordinate wheel controller is required to set the specified slip values, phase shifts between the setpoint and actual value are inevitable. This can be taken into account when designing the vehicle controller by including the typical wheel controller dynamics in the model. However, this leads to a higher system order and this can lead to computing time problems. Alternatively, the phase shift of the lower-level controller can be approximately compensated for by introducing a D component in the feedback of the state variables. The rule set is then: $$\underline{\mathit{\text{U}}}\text{= -}\mathit{\text{F}}\text{(}\underline{\mathit{\text{X}}}\text{+}{\mathit{\text{K}}}_{\mathit{\text{D}}}\text{·}\underline{\dot{\mathit{\text{X}}}}\text{).}$$

Terms used:

  - Sollschlupf
V _Ri   - Radgeschwindigkeit
P  - Vordruck
P _i   - Radbremsdruck
F _R   - Gesamtkraft des Reifens
a _X , a _Y - longitudinal / lateral acceleration in the center of gravity
C _λ , C _α - longitudinal / lateral stiffness of the tire
F _Bi , F _Si - tire forces in the longitudinal / transverse direction of the tire
F _Xi , F _Yi - tire forces in the vehicle's longitudinal / transverse direction
F _Zi - tire contact force
m - vehicle mass
S _i - Resulting tire slip
V _X , V _Y - vehicle longitudinal / lateral speed in the center of gravity
V̇ _X , V̇ _Y - change over time in the longitudinal / transverse speed
V _Xi , V _Yi - vehicle longitudinal / lateral speed on the wheel
V _Ch - Characteristic speed V _Ch - Characteristic speed
α _i - slip angle of the wheel
β - the vehicle's swimming angle in the center of gravity
δ - steering angle (front)
δ _H - steering angle on the rear wheels
ψ̇ - yaw rate
λ _i - tire slip
» _Ri - Resulting adhesion coefficient
ϑ - moment of inertia around vehicle vertical axis
l _V , l _H , l _L , l _R - geometric dimensions (center of gravity)
A , B , ... - Matrices
a , b , X ... - vectors
λ

- Target slip
V _Ri - wheel speed
P - form
P _i - wheel brake pressure
F _R - total force of the tire

Claims (2)

1. Method for improving the controllability of motor vehicles, desired slip values λ

   

   being determined for the individual wheels with the aid of the measured variable of yaw rate ψ̇ and the longitudinal speed V _X determined and the wheel slips being adjusted accordingly at at least some of the wheels by means of an antiblock control system or drive slip control system, characterised in that, in addition to the measurement variable of yaw rate ψ̇, the wheel speeds V _Ri , the steering angle δ, the inlet pressure P or the wheel brake cylinder pressure P _i and, in a drive slip control system, the engine speed and the throttle valve angle are measured, in that the longitudinal vehicle speed V̂ _X , the longitudinal vehicle acceleration

   

   _X , the wheel slip values λ _i and the tyre forces in the tyre longitudinal direction F̂ _Bi are estimated herefrom, in that these variables V̂ _X ,

   

   _X and λ _i are fed to a vehicle controller and the variables V̂ _X , λ _i and F̂ _Bi are fed to an observer for estimating the total force F̂ _R and the transverse speed V̂ _Y , which observer then passes the latter on to the vehicle controller, and in that desired slip values λ

   

   at the wheels are determined in the vehicle controller with the aid of a simple model, and are adjusted using an antiblock control system or drive slip control system.
2. Method according to Claim 1, characterised in that the desired slip values are fed to an antiblock/drive slip control system, which for its part gererates desired slip values, and in that the deviation of one desired slip value from the other is superimposed thereupon.

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